Positioning satellite system for measuring position of signal source

ABSTRACT

A satellite system includes a signal source located on a surface of the earth, a surface of water, or in air; an orbiting satellite for measuring a position of the signal source, having a GPS receiver which receives a GPS signal from a GPS satellite system to measure the position of the orbiting satellite, a frequency measuring device for receiving the radio wave signal emitted from the signal source to measure the frequency thereof, a memory for storing frequency data and position data, and a transmitting device for transmitting the data stored in the memory toward the earth; and a ground station, having a signal receiving device for receiving the data transmitted from the orbiting satellite, including a computer for calculating the position of the signal source based on the data received by the signal receiving device.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is entitled to the benefit of the filing date of, andhereby incorporates by reference the subject matter disclosed in,Japanese Patent Application No. 11-282359 filed on Oct. 4, 1999, as wellas International Application No. PCT/JP00/06897 filed on Oct. 4, 2000.

FIELD OF THE INVENTION

The present invention relates to a positioning method and an apparatusto measure a position of a signal source moving on the earth's surface,on the surface of water, or in the air.

BACKGROUND OF THE INVENTION

In recent years, a position tracking system to track the movement ofwild animals in order to protect the same, and for ecological researchthereof, has been developed. For instance, to research the ecology andbehavior of whales, a transmitter is attached to a whale, so that aradio wave output from the transmitter is received by a receiverprovided in an aircraft or a vessel to obtain positional data of thetransmitter to thereby track the position of the whale. In this trackingsystem, it is impossible to simultaneously track a number of individualwhales ranging over a large area. Furthermore, the tracking system usingan aircraft or vessel is suitable for tracking for a short period oftime, but it is difficult to continuously carry out the tracking for along time, e.g., several months. Moreover, it is extremely difficult totrack birds having a high moving speed and wide home range even for ashort period of time. In addition, data obtained by the tracking must betransferred from the aircraft or vessel to researchers in a groundfacility by a transmission device, which proved to be very inconvenient.

A portable GPS (Global Positioning System) receiver which is designed toreceive a GPS signal from a GPS (NAVSTAR) satellite in order to obtainpositional data has been developed. However, it is necessary for the GPSreceiver to receive GPS signals from at least four satellites in orderto measure a position on earth. To this end, the GPS receiver mustreceive the GPS signals for a long time. Therefore, it is difficult totrack an animal such as a whale that appears on the sea surface for avery short period.

Moreover, it is difficult to miniaturize an antenna of the GPS receiverwhich receives weak GPS signals, and accordingly, it is difficult tomake a small GPS receiver. This makes it impossible to attach the GPSreceivers to small animals such as birds.

SUMMARY OF THE INVENTION

It is an object of the present invention to eliminate the drawbacksmentioned above by providing a positioning satellite system in which theposition of an animal can be continuously tracked for a long time,regardless of the speed or range of the movement of the animal, and inwhich the signal source to be attached to the animal can be made small.

To achieve the object mentioned above, according to an aspect of thepresent invention, a satellite system is provided, including a signalsource located on or in at least one of a surface of the earth, asurface of water, and the air, the signal source including a transmitterdevice for emitting a radio wave signal having a predetermined frequencyand an identification code corresponding to a specific objective; anorbiting satellite for measuring a position of the signal source, theorbiting satellite including a GPS receiver which receives GPS signalsfrom a GPS satellite system to measure the position of the orbitingsatellite, a frequency measuring device for receiving the radio wavesignal emitted from the signal source to measure the frequency of theradio wave signal, a memory for storing frequency data measured andobtained by the frequency measuring device and position data measuredand obtained by the GPS receiver upon measurement of the frequency ofthe radio signal, and a transmitting device for transmitting the datastored in the memory toward the earth's surface; and a ground stationhaving a signal receiving device for receiving the data transmitted fromthe orbiting satellite, the ground station including a computer forcalculating the position of the signal source based on the received dataof the signal device.

Preferably, the frequency measuring device includes a phase-lock loopreceiver.

Preferably, the frequency measuring device and the GPS receiver carryout several measurements of the radio wave signals emitted from the samesignal source during the movement of the orbiting satellite, on andalong the same orbit, on which the frequency measuring device and theGPS receiver are provided so that the measurement data of eachmeasurement is stored in the memory.

Preferably, the orbit of the orbiting satellite is a polar orbit orsub-recurrent orbit.

The computer can measure the position of the signal source based onreference frequency data of the radio wave signal emitted from thesignal source; wherein the frequency data is measured by the frequencymeasuring device, and the position data of the orbiting satellite ismeasured by the GPS receiver.

Preferably, the orbiting satellite includes a signal receiving devicefor receiving the radio wave signal emitted from the ground station; theground station including a transmitting device for transmitting aspecific command to send the data stored in the memory of the orbitingsatellite; and the orbiting satellite transmitting the data stored inthe memory via the transmitting device upon receipt of the specificcommand through the signal receiving device.

Preferably, when the radio wave signal of the predetermined frequency isemitted, the signal source sends an identification signal to identifythe signal source by the radio wave signal.

According to another aspect of the present invention, a satellite systemis provided, including a signal source located on or in at least one ofa surface of the earth, a water surface, and the air; and an orbitingsatellite for measuring a position of the signal source, the orbitingsatellite including a GPS receiver which receives GPS signals from a GPSsatellite system, a frequency measuring device for receiving a radiowave signal emitted from a ground signal source on the earth to measurethe frequency of the radio wave signal, a memory for storing frequencydata measured and obtained by the frequency measuring device andposition data measured and obtained by the GPS receiver upon measurementof the frequency, and a transmitting device for transmitting the datastored in the memory toward the earth's surface.

According to another aspect of the present invention, a ground stationis provided, including a signal receiving device for receiving datatransmitted from an orbiting satellite; and a computer for analyzing thedata received by the receiving device. The orbiting satellite includes aGPS receiver which received the GPS signals from a GPS satellite systemto measure the position of the orbiting satellite; a frequency measuringdevice for receiving the radio wave signal emitted from signal sourcelocated on or in at least one of a surface of the earth, a surface ofwater, and the air, to measure the frequency of the radio wave signal; amemory for storing frequency data measured and obtained by the frequencymeasuring device and position data measured and obtained by the GPSreceiver upon measurement of the frequency of the radio signal; and atransmitting device for transmitting the data stored in the memorytoward the earth's surface.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be discussed below in detail with reference to theaccompanying drawings, in which:

FIG. 1 is a schematic view of an embodiment of a positioning satellitesystem according to the present invention;

FIG. 2 is a schematic view of an embodiment of a positioning satellitesystem according to the present invention;

FIG. 3 is an exploded perspective view of a satellite according to thepresent invention;

FIG. 4 is a block diagram of a control system for a satellite shown inFIG. 3.

FIG. 5 is a chart showing the relationship between true and max, whereinthe solid line and the dotted line represent φ_(true)=0 and φ_(true)=π,respectively;

FIG. 6 is a chart showing a profile of the proximity function F (θ, φ),in which the measured Doppler coefficient {ε_(n) ^(meas)} includes thestandard deviation 10⁻⁹ mixed therein;

FIG. 7 is a chart showing 32 points corresponding to the Doplercoefficient {ε_(n) ^(true)}_(n=1−11) generated by changing the noisecomponent;

FIG. 8 is a chart showing the relationship between the precision limitand the noise level;

FIG. 9 is a chart showing the results obtained when 13 measurements ofthe Doppler coefficients were carried out in a measurement distance of[φ₁, φ₁₃]=[−3°, 3°]; and

FIG. 10 is a chart showing the relationship between the precision limitand the noise level, wherein the change in Δ is not ignored.

DESCRIPTION OF THE PREFERRED EMBODIMENT

FIGS. 1 and 2 show an embodiment of the present invention, applied to awhale ecology observation satellite (WEOS).

An artificial satellite (orbiting satellite) 100 is a polar orbitsatellite which orbits over the North Pole and the South Pole of theearth 10 and moves over a base station 300 as a ground facility on theearth 10 at a predetermined period. The altitude and speed of thesatellite 100 are approximately 800 km and 8 km/sec, respectively. Notethat the orbit is preferably a polar orbit, however the presentinvention can be applied to any orbit other than the polar orbit, forexample, a sub-recurrent orbit. Also, the altitude is not limited to aspecific value.

The satellite 100 is provided with a GPS receiver 133 (see FIG. 4) whichreceives GPS (Global Positioning System) signals from twenty four GPS(NAVSTAR) satellites 401, 402, 403, 404, 405, 406 . . . which are higherthan the satellite 100 to measure its own orbital coordinates (altitude,latitude and longitude). Only six GPS (NAVSTAR) satellites are shown inFIG. 2. The satellite 100 is also provided with a Doppler shift receiverwhich receives measuring radio wave (uplink signal) T3 of a specificfrequency (around 400 MHz), output from a signal source 200 on the earth10 to measure a frequency shift. The signal source 200 repeatedly emitsthe measuring radio wave T3 at a predetermined time interval. Thesatellite 100 obtains frequency data (or frequency shift data) of themeasuring radio wave T3, and coordinate data of the satellite 100, everytime the satellite 100 receives the measuring radio wave T3, and thedata is stored in a memory provided in the satellite 100.

The base station 300 outputs a data transmission command radio wave C3to the satellite 100 via the parabolic antenna (transmitting device) 301when the satellite 100 moves over the base station. When the satellite100 receives the data transmission command radio wave C3, the datastored in the memory of the satellite 100 is transmitted toward theearth (base station 300) by an antenna (transmitting device) 127 via thesignal radio wave T1. The base station 300 receives the signal radiowave T1 via the parabolic antenna (signal receiving device) 301.Consequently, the position (coordinates) of the signal source 200 iscalculated based on the frequency shift data, the coordinate data of thesatellite 100, and the speed data of the satellite 100 by a computerprovided in the base station 300.

The signal source 200 is a transmitter which repeatedly outputs themeasuring radio wave T3 of the specific frequency (about 400 MHz) at apredetermined time interval. The measuring radio wave T3 carries atleast identification code data assigned to each signal source 200. Thesignal source 200 outputs the measuring radio wave T3 at a predeterminedtime interval while a whale 20 appears on the sea surface and theantenna (emitter device) 201 of the signal source 200 extends upwardfrom the sea surface.

The signal source 200 in the illustrated embodiment is incorporated inan ecological study probe for a whale 20. The ecological study probe isprovided therein, for example, with a pressure sensor to measure thediving depth of the whale, a temperature sensor, a microphone to pickupthe call of the whale, a memory in which data detected or obtained bythe sensors and the microphone is stored as digital signals, and abattery as a power source for the same, etc. The data thus obtained istransmitted when the measuring radio wave T3 is transmitted from thesignal source 200.

FIG. 3 shows an exploded perspective view of the main components of thesatellite 100. The satellite 100 is comprised of a body 101 and anattitude control mast 103 (see FIG. 1). The body 101 is provided on itscenter with a box 111 having a square section, a top plate 105 and abottom plate 107 attached to the upper and lower ends of the box 111,and four solar panels 109 which are secured at their upper and loweredges to the top and bottom plates 105 and 107 to surround the box 111.The extendable attitude control mast 103 is secured to the upper end ofthe box 111. The box 111 is provided with main electronic elements 130.Other electronic parts are arranged in a space defined between the box111 and the solar panels 109. The attitude control mast 103 extendsoutward through a central hole formed in the top plate 105. Note thatthe attitude control mast 103 is shown in a retracted position in FIG.3.

A GPS antenna 121 is attached to the outer surface of the top plate 105which is oriented in an opposite direction to the earth. Four antennaelements 124 (see FIG. 3) which operate in a UHF band have twofunctions, one function is to receive the radio wave T3 for measuringthe frequency through antennas 123 (of FIG. 4), and the other functionis to receive the command radio wave C3 through antenna 125 (of FIG. 4).The antenna (transmitting device) 127 which transmits a signal radiowave T1 is secured to the outer surface of the bottom plate 107 whichfaces the earth 10. The body 101 is also provided with a torque coil 113which is adapted to control the attitude of the satellite 100 so thatthe axis thereof is oriented toward the center of the earth 10.

The main electronic elements 130 of the satellite 100 are shown in ablock diagram of FIG. 4. The satellite 100 is generally controlled by amicro computer (CPU) provided in a control circuit (controller) 135. Themeasuring radio wave T3 emitted from the signal source 200 is receivedby the antennas 123 and is distributed to a PLL receiver (phase-lockloop receiver/frequency measuring device) 131 via an HYB circuit 129.The PLL receiver 131 controls the oscillation frequency so that thephase of the frequency is synchronized with the phase of the inputmeasuring radio wave T3. The controlled frequency is stored in a memory137 as measured frequency data. By counting the frequency fo thecontrolled oscillator in synchronization, a Doppler frequency shiftcorresponding to the slant range rate between the satellite 100 and thesignal source 200 is readily obtained.

The satellite 100 which receives the measuring radio wave T3 receivesthe GPS signals emitted from the GPS satellites 401, 402, 403, 404, 405,406, . . . via the GPS antenna 121, so that the GPS receiver 133calculates the position (orbital coordinates of latitude and longitude)of the satellite 100. The calculated data is written in the memory 137as position data of the satellite 100 upon measurement of the measuringfrequency data.

The control circuit 135 repeatedly carries out the operations mentionedabove every time the control circuit 135 receives the measuring radiofrequency T3, and stores the measurement time, the measured frequencydata, and the measured position data in the memory 137.

A predetermined command is carried and sent by the command radio wave C3to the satellite 100 when the satellite 100 travels above the basestation 300. The control circuit 135 analyzes the command radio wave C3which has been received by the antenna 125 and distributed by the HYBcircuit 129. If the signal represents a predetermined command, all themeasured frequency data and position data stored in the memory 137 aresent by modulating the signal radio wave T1 which is output through theantenna (transmitting device) 127.

The base station 300 receives the measured frequency data and positiondata, etc., carried by the signal radio wave T1 emitted from thesatellite 100 and stores the same in a memory of the base-stationcomputer. Consequently, the position (orbital coordinates of latitudeand longitude) of the signal source 200 is calculated based on theplural sets of measured frequency data and position data, obtainedwithin a predetermined time.

As can be understood from the foregoing, the observer can determine theposition of the whale 20 at any position on the earth. Since the signalsource 200 is only required to periodically emit a weak radio wave, in ashort space of time, which can be received by the satellite 100 it ispossible to miniaturize the components including the battery therefor.Therefore, it is possible to track and observe the position and movementof not only large-sized animals such as whales but also small-sizedanimals, for example, migratory birds such as cranes or wild geese.Moreover, since the satellite 100 in the illustrated embodiment orbitsthe earth along a polar orbit, one satellite 100 and one base station300 can cover the whole earth.

The position detection method of the signal source 200 will be discussedhereinafter. In the illustrated embodiment, when the satellite 100 movesover the base station 300, the PLL receiver 131 of the satellite 100receives the measuring radio waves T3 transmitted from the base station300 as reference data at a predetermined time interval. The frequency ofthe measuring radio wave T3 and the position of the satellite 100 aremeasured every time the satellite receives the measuring radio wave. Themeasurement data is stored in the memory 137. The measurement of theposition will be discussed below in detail.

It is assumed that the distance between the satellite 100 and the signalsource 200 is D(t;Pt), wherein “t” represents the time at the satellite100 and “PT” represents the position of the signal source 200. Theangular acceleration D of the satellite 100 is given by D=dD/dt. Thus,the following formula (1) is obtained, provided that the relative effectis ignored.

f _(R)(t;P _(T))={1+ε(T;P _(t))}f _(T)

ε(t;P _(t))=−C ⁻¹ D(t;P _(t))  (1)

wherein “fT” represents the frequency of the measuring radio wave T3,“fR” represents the frequency of the radio wave received by thesatellite 100, “C” represents the velocity of light, and “ε” representsthe Doppler coefficient, respectively.

The frequency f_(T) fluctuates within the range of a design value fo.The frequency f_(L) is a reference frequency used to measure thefrequency f_(R) in the satellite 100. For convenience sake, the standardfrequency deviations of the frequencies f_(T) and f_(L) are δ_(T),δ_(L), respectively, the following expressions are given by thefollowing equation (2);

f _(T) =fo(1+δ_(T))

f _(L) =fo(1+δ_(L))  (2)

The Doppler shift is defined by a difference between the frequenciesf_(R) and fT, which can be obtained by the above expressions. Therefore,the following equation (3) is obtained using the measured Doppler shift(f_(R)−f_(L)) as “an apparent Doppler coefficient”. $\begin{matrix}\begin{matrix}{{\hat{ɛ} \equiv \quad \frac{f_{R} - f_{L}}{f_{0}}} = \frac{{\left( {1 + ɛ} \right)f_{r}} - f_{L}}{f_{0}}} \\{= \quad {{{\left( {1 + ɛ} \right)\left( {1 + \delta_{T}} \right)} - \left( {1 + \delta_{L}} \right)} \approx {ɛ + \left( {\delta_{T} - \delta_{L}} \right)}}}\end{matrix} & (3)\end{matrix}$

Since ε and δT are both smaller than 1, εδ_(T) is negligible. Inpractice, many factors have an influence on the measurement of theDoppler coefficient ε. If the possible influences are all treated aseffective noise ν, the following equation (4) is obtained.$\begin{matrix}\begin{matrix}{ɛ^{meas} = \quad {{\hat{ɛ} + v} = {ɛ + \Delta + v}}} \\{\Delta \equiv \quad {\delta_{T} - \delta_{L}}}\end{matrix} & (4)\end{matrix}$

In general, the stability of the signal source 200 and the satellite 100in the short oscillation period is extremely high, and hence, thevariation Δ during the measurement of the position is negligible.Consequently, the variation Δ can be considered an unknown constant.

It is assumed that “ε_(n)” represents the n^(th) Doppler coefficientmeasured at the sampling time t_(n). Assuming that the signal source 200is at the position P1, the Doppler coefficient is given by{ε(t_(n);P_(T))+Δ}. Therefore, the square deviation between the Dopplercoefficient and the actual measurements at the N sampling points isgiven by the following equation (5): $\begin{matrix}{{S\left( {P_{T},\Delta} \right)} = {\sum\limits_{n = 1}^{N}\quad \left\{ {{ɛ\left( {t_{n};P_{T}} \right)} + \Delta - ɛ_{n}^{meas}} \right\}^{2}}} & (5)\end{matrix}$

If S is minimum at (P_(t), Δ) =(P_(T) ^(min), Δ^(min)), it can bepresumed that the value of P_(T) ^(min) represents the correct positionof the signals source 200. However, since S is a square-function of Δ, Sis minimum when Δ satisfies the following equation (6). $\begin{matrix}{{{\Delta^{optm}\left( P_{T} \right)} = {\frac{1}{N}{\sum\limits_{n = 1}^{N}\quad \left\{ {ɛ_{n}^{meas} - {ɛ\left( {t_{n};P_{T}} \right)}} \right\}}}},} & (6)\end{matrix}$

The minimum value is given by the following equation (7):$\begin{matrix}\begin{matrix}{{F\left( P_{T} \right)} \equiv \quad {S\left( {P_{T},{\Delta^{optm}\left( P_{T} \right)}} \right)}} \\{= \quad {{\sum\limits_{n = 1}^{N}\quad \left\{ {ɛ_{n}^{meas} - {ɛ\left( {t_{n};P_{T}} \right)}} \right\}^{2}} - {N\left\{ {\Delta^{optm}\left( P_{T} \right)} \right\}^{2}}}}\end{matrix} & (7)\end{matrix}$

Therefore, in the illustrated embodiment, it is necessary only to obtainthe proximity function F(P_(T)), in place of S(P_(T), Δ) in order toobtain P_(T) ^(min).

The practical theory will be discussed below.

In general, the center of gravity of the earth can be determined basedon the coordinate system. If the Z-axis is selected to be the directionof the angular momentum of the satellite 100, and the X-axis is selectedto be the major axis of the orbit, the position r_(s) of the satellite100 is defined by the following formula (8): $\begin{matrix}{{r_{s} = {\begin{pmatrix}x_{s} \\y_{s} \\z_{s}\end{pmatrix} = \begin{pmatrix}{r\quad \cos \quad \phi} \\{r\quad \sin \quad \phi} \\0\end{pmatrix}}},{r = \frac{a\left( {1 - ^{2}} \right)}{1 + {\quad \cos \quad \phi}}}} & (8)\end{matrix}$

φ represents the zenith angle, “a” represents the mean radius of theorbit, and e represents the eccentricity of the orbit, respectively.

The time derivative of φ is given by the following formula (9).$\begin{matrix}{\overset{.}{\phi} = \frac{\sqrt{{GMa}\left( {1 - ^{2}} \right)}}{r^{2}}} & (9)\end{matrix}$

wherein G represents the gravitational constant and M represents theweight of the earth, respectively.

Since r relies only upon the time t via φ, r can be obtained by thefollowing equation (10), as a result of the formula 8: $\begin{matrix}{r = {{\frac{r}{\phi}\overset{.}{\phi}} = {\frac{{r}^{2}\quad \sin \quad \phi}{a\left( {1 - ^{2}} \right)}\overset{.}{\phi}}}} & (10)\end{matrix}$

The position P_(T)=r_(T) of the signal source 200 can be limited to thatof the earth surface, the position of the signal source 200 can besimplified using polar coordinates (Θ, Φ). If R designates the radius ofthe earth, the distance D(t;P_(T)) between the satellite 100 and thesignal source 200 is obtained by the following expression (11):$\begin{matrix}\begin{matrix}{{D\left( {t;P_{T}} \right)} = {{r_{s} - r_{T}}}} \\{= \sqrt{R^{2} + r^{2} - {2{Rr}\quad \sin \quad {{\Theta cos}\left( {\phi - \Phi} \right)}}}}\end{matrix} & (11)\end{matrix}$

The velocity in the radial direction is obtained by the followingexpression (12): $\begin{matrix}\begin{matrix}{{\overset{.}{D}\left( {t;P_{T}} \right)} = \frac{{D\left( {t;P_{T}} \right)}}{t}} \\{= \frac{{r\overset{.}{r}} - {R\overset{.}{r}\quad \sin \quad {{\Theta cos}\left( {\phi - \Phi} \right)}} + {{Rr}\quad \sin \quad {{\Theta sin}\left( {\phi - \Phi} \right)}\overset{.}{\phi}}}{\sqrt{R^{2} + r^{2} - {2{Rr}\quad \sin \quad {{\Theta cos}\left( {\phi - \Phi} \right)}}}}}\end{matrix} & (12)\end{matrix}$

If we substitute formula 12 for formula 10, the following formula 13 isobtained. $\begin{matrix}\begin{matrix}{{ɛ\left( {t;P_{T}} \right)} \equiv \quad {- \frac{\overset{.}{D}\left( {t;P_{T}} \right)}{c}}} \\{= \quad {\beta \frac{{\left\{ {{{\rho sin}\left( {\Phi - \phi} \right)} + {{\lambda cos}\left( {\Phi - \phi} \right)}} \right\} \sin \quad \Theta} - {\lambda\rho}}{\sqrt{1 + \rho^{2} - {2{{\rho sin\Theta cos}\left( {\Phi - \phi} \right)}}}}}}\end{matrix} & (13)\end{matrix}$

The non-dimensional variables p, β, λ are defined by the followingexpressions (14): $\begin{matrix}\begin{matrix}{{{\rho \equiv \quad \frac{r}{R}} = \frac{\gamma}{1 + {cos\phi}}},\quad {\beta \equiv {\frac{1}{c}\sqrt{\frac{\gamma \quad {GM}}{R}}\frac{1}{\rho^{2}}}}} \\{\lambda \equiv \quad {\frac{e}{\gamma}\rho^{2}\sin \quad \phi}}\end{matrix} & (14)\end{matrix}$

wherein γ is a non-dimensional variable as defined in Equation 15 below.$\begin{matrix}{\gamma \equiv \frac{a\left( {1 - ^{2}} \right)}{R}} & (15)\end{matrix}$

When e=0, as in a circular orbit, the variables ρ and β are notdependent upon time, and hence λ=0. However, in general, β, λ and ρ aredependent upon time via φ. In any case, the proximity function F can beexpressed by a function (Θ, φ) which is obtained by substitutingequation 13 for equation 7. The position of the signal source 200 can beestimated by minimizing the two variables of the proximity function F(Θ, φ).

ε(t;Pr) is dependent only upon Θ through sin Θ, as can be seen inequation 13.

F(Θ, φ)=F(π−Θ, φ)  (16)

If equation 16 is satisfied and (Θ^(min), φ^(min)) minimizes theproximity function F (π−Θ^(min), φ^(min)) becomes minimum. If thesatellite 100 orbits over the signal source 200, the previous proximatecalculation result and the current proximate calculation result arecompared in the position measuring operation to obtain the two minimumpositions.

On the assumption that the radial distance from the center of the earthto the signal source 200 is r, if the requirement of (D²≦r²−R²) issatisfied, it is possible to receive the signal from the signal source200 on the sea. According to equation 11, the requirement is expressedby the following equation (17):

1+e cos φ≦γ sin Θ cos(Θ−Φ)  (17)

For example, when Θ=0, or Θ=π (when the signal source 200 is located inthe X-Z plane), equation 17 can be replaced with the following equation18. $\begin{matrix}{{\cos \quad \phi} \geq \frac{1}{{\gamma sin\Theta} \mp }} & (18)\end{matrix}$

wherein the negative sign corresponds to φ=0. So long as Θ satisfiesequation 19, equation 18 can be used as a practical solution to obtainΘ. $\begin{matrix}{{\Theta \geq {\sin^{- 1}\frac{1 \pm }{\gamma}}} = {\sin^{- 1}\frac{R}{a\left( {1 \mp } \right)}}} & (19)\end{matrix}$

The foregoing has been applied to a method for determining anapproximate position of the signal source 200 using the Doppler effect.The accuracy of this method for determining the position of the signalsource 200 will be discussed below.

It is assumed that the orbit of the satellite 100 is an elliptical orbit(apoapsis “a”=7178 km , eccentricity “e”=0.01393) in which the maximumaltitude is 900 km, and minimum altitude is 700 km. First, the Dopplercoefficient {ε_(n) ^(true)}_(n=1˜N) at {t_(n)}_(n=1˜N) is calculatedwhen the true position of the signal source 200 is given by (Θ_(true),φ_(true)). Consequently, for all the variables which depend upon thetime via φ, {φ_(n)}_(n=1˜N) is used in place of {t_(n)}_(n=1˜N). Sincethe sampling points {φ_(n)}_(n=1˜N) are assumed to be regular, the pitch[Θ1, ΘN] corresponds to the “measurement pitch”, and accordingly, allthe measurements are carried out at this pitch. To simulate the Dopplercoefficient {ε_(n) ^(true)}_(n=1˜N), noise and a constant Δ are added tothe Doppler coefficient {εn^(true)}_(n=1˜N). The minimum position of theproximity function at which F (Θ_(min), φ_(min)) is minimum is comparedwith the true position (Θ_(true), φ_(true)).

The noise is presumed using the Gaussian with zero mean. The standarddeviation fluctuates in the range of 10⁻¹⁰˜10⁻⁸, according to the PLLreceiver 131 which can measure the frequency of 400 MHz in the order of0.1 Hz.

The designator Δ which is used to explain the fluctuation of thefrequency has no influence on the precise position measurement so longas it is constant, as can be seen from the fact that the quadraticexpression 7 was deleted from equation 5. All the results shown belowexcept Table 6 can be presumed by Δ=10⁻⁶, however similar results can beobtained when Δ is assumed to be zero.

As can be understood from the above discussion, the satellite 100 canreceive the signal from the signal source 200 when the satellite 100satisfies the expression 17. Therefore, true position (θ_(true),φ_(true)) of the signal source 200 can be measured when φ satisfies theexpression 17 in the predetermined distance [φ_(min), φ_(max)] including[φ1 φN}. For example, in φ_(true)=0 or φ_(true)=π, the maximum value ofθ_(true) is obtained based on equation 19 and the distance [φ_(min),φ_(max)] for φ_(true) can be determined based on equation 18. In thiscase φ_(min) is identical to −φ_(max) and the relationship betweenθ_(true) and φ_(max) is shown in FIG. 5. In FIG. 5, the solid line andthe dotted line represent φ_(true)=0 and φ_(true)=π, respectively. Forexample, when φ_(true)=0, θ_(true) must be greater than 64 degrees. Ifθ_(true) is selected to be identical to 70 degrees, φ_(min)=17 degrees.This means that when the signal source 200 is at the position of(θ_(true), φ_(true))=(70°, 0°), the sampling points {φ_(n)}_(n=1˜N) mustbe located in the interval [−17°, 17°].

In the simulation, when the position (θ_(true), φ_(true)) of the signalsource, obtained based on the true positions (θ_(true), φ_(true)) ofmany signal sources 200, the sampling points {ψ_(n)}_(n=1˜N), and noiselevels was (80°, 10°), the 11 Doppler coefficients were measured, andthe distance [ψ1, ψ11] was equal to the [−5°, 5°], the typical resultsas shown in Tables 2 through 5 were obtained. The satellite 100 moved bythe abovementioned distance in about 163 seconds.

FIG. 6 shows a profile of the proximity function F (θ, φ), in which themeasured Doppler coefficient {ε_(n) ^(meas)} includes the standarddeviation 10⁻⁹ mixed therein.

The gray scale represents the value of the proximity function F. Thedarker the gray scale, the smaller the value. The horizontal axis(abscissa) represents (θ−θ_(true)), and the vertical axis (ordinate)represents (φ−φ_(true)), respectively. The unit of measured value is[mdeg]. In FIG. 6, 1 Mdeg=0.001° corresponds to 111 m on the earthsurface. It is found from FIG. 6 that the minimum point (θ_(min),φ_(min)) is adjacent the true position (θ_(true), φ_(true)).

If the noise component in the Doppler coefficient {ε_(n)^(true)}_(n=1˜N) changes, the profile of the proximity function isslightly distorted, so that the minimum point (θ_(min), φ_(min)) movesaround the true position (θ_(true), θ_(true)). For instance, if thenoise level is maintained to be 10⁻⁹ and 32 sets of the Dopplercoefficient {ε_(n) ^(true)}_(n=1˜N) is generated by changing the noisecomponent, 32 minimum points corresponding to each case are plotted inFIG. 7.

The minimum points are distributed around the true position within ±20mdeg in the Θ-axis direction and within ±2 mdeg in the φ-axis direction.In the evaluation of the correct position, based on the standarddeviation along each axis, the respective values are 7.3 mdeg and 0.72mdeg. In order to minimize the proximity function, a function analysissoftware was used to obtain the minimum value. Four points(Θ_(true)±10°, φ_(true)±10°) were used as initial positions. However, itwas found that the values were always concentrated to the same point inthe repetitive measurements.

FIG. 8 shows a relationship between the precision limit and the noiselevel. In FIG. 8, σ_(θ)σ_(φ) represent the standard deviations ofθ_(min)φ_(min), respectively. (θ_(min), φ_(min)) is a mean value of(θ_(min), φ_(min)) and is referred to as <mean evaluation position>. Onthe assumption that the mean value δ_(mean) shown in FIG. 8 is adeviation of (θ_(min), φ_(min)) from (θ_(true), φ_(true)), followingequation (20) is set. $\begin{matrix}{\delta_{mean} \equiv \sqrt{\left( {{\overset{\_}{\Theta}}_{\min} - \Theta_{true}} \right)^{2} + \left( {{\overset{\_}{\Phi}}_{\min} - \Phi_{true}} \right)^{2}}} & (20)\end{matrix}$

Equation 20 shows the measure of the bias of the evaluated values.

Thirty two calculations of (Θ_(min), φ_(min)) are repeated for eachnoise level to calculate σ_(Θ), σ_(φ) and δ_(mean). Namely, σ_(Θ) andσ_(φ) are both proportional to the noise level or the standard deviationof the noise.

The results obtained when 13 measurements of the Doppler coefficientswere carried out in a measurement distance of [φ₁, φ₁₃]=[−3°, 3°] areshown in FIG. 9. The satellite 100 passed the measurement distance in 98seconds. In this case, the sampling number N=13 was larger than that inthe previous case but the distribution of the sampling points is limitedto a narrow area. Moreover, similar to δ_(mean), the values of σ_(θ) andσ_(φ) are larger than those in FIG. 8.

According to the method of the present invention, a change in Δ can beignored during the position measuring operation. However, In the actualmeasurement, a change inevitably occurs. In a precise simulation of themeasurement, the measurement is influenced by change. To obtain theresult shown in FIG. 8, Δ was linearly increased by 10⁻⁹ during themovement of satellite 100 in the distance [−5°, 5°]. The results thereofare shown in FIG. 10. In FIG. 10, σ_(θ) and σ_(φ) are almost identicalto those in FIG. 8, but δ_(mean) is considerably greater than that shownin FIG. 10. This means that the minimum position (θ_(min), φ_(min)) inconnection with the proximity function caused the evaluation of theposition of the signal source 200 to be deviated if Δ changes during themeasurement of the position. The larger the change of Δ, the greater thedeviation of the evaluation.

As can be understood from the above discussion, according to theposition measuring satellite system of the present invention, it can beseen from FIGS. 8 and 9 that if the period of time in which the whaleappears on the sea surface is extremely short, the measurement intervalis shortened, so that the position measurement error of the signalsource 200 is increased. However, according to the whale's generalbehavior, the whale dives in the sea and thereafter rises to the sea ina few minutes at a point not far from the diving point. If the risingpoint is out the measurement range, the measurement distance [φ₁, φ_(N)]is increased, but the Doppler coefficient is measured again, In anyevent, if the range of (φ_(N)−φ₁) is not similar than 10°, and thestandard deviation of the noise is not greater than 10⁻⁹, the positionmeasurement errors σ_(θ) and σ_(φ) of the signal source 200 are lessthan 5 mdeg=500 m, as shown in FIG. 8, and are comparable to the priorart (e.g., Argos [3]).

As can be understood from the foregoing, according to the positionmeasuring satellite system of the present invention, since the signalsource is only required to emit the signal radio wave, it is possible tomeasure the position of an animal even if it appears on the sea surfacewithin a very short space of time, such as a whale, by emitting thesignal radio wave for a time long enough to specify the position of thesignal source. Moreover, if the satellite moves along a polar orbit, itis possible to cover the overall surface of the earth by a single basestation.

According to the above description, the signal radio wave emitted fromthe signal source is received to measure the frequency thereof; theposition of the satellite is precisely measured by the GPS receiverprovided on the satellite; the measurement data is stored in the memory;the stored data is transmitted to the apparatus on the earth; and theposition of the signal source is measured by the apparatus on the earth.Moreover, since the signal source is only required to emit the signalradio wave, the signal source can be made small and light, so that theservice life of the batteries can be prolonged, whereby the measurementcan be carried out for a long time.

Obvious changes may be made in the specific embodiments of the presentinvention described herein, such modifications being within the spiritand scope of the invention claimed. It is indicated that all mattercontained herein is illustrative and does not limit the scope of thepresent invention.

What is claimed is:
 1. A satellite system comprising: a signal sourcelocated on or in at least one of a surface of the earth, a surface ofwater, and the air, said signal source including an emitter device foremitting a radio wave signal having a predetermined frequency; anorbiting satellite for measuring a position of said signal source, saidorbiting satellite including a GPS receiver which receives a GPS signalfrom a GPS satellite system to measure the position of said orbitingsatellite, a frequency measuring device for receiving the radio wavesignal emitted from the signal source to measure the frequency of saidradio wave signal, a memory for storing frequency data measured andobtained by the frequency measuring device and position data measuredand obtained by the GPS receiver upon measurement of the frequency ofsaid radio signal, and a satellite transmitting device for transmittingfrom said orbiting satellite the data stored in said memory toward theearth's surface; and a ground station having a ground-station signalreceiving device for receiving said data transmitted from said orbitingsatellite, said ground station comprising a computer for calculating theposition of said signal source based on the received data of said signalreceiving device, and a ground-station transmitting device fortransmitting a specific command to send the data stored in said memoryof the orbiting satellite; said orbiting satellite including a satellitesignal receiving device for receiving the radio wave signal emitted fromthe ground station; and said orbiting satellite transmitting the datastored in the memory via the satellite transmitting device upon receiptof the specific command through the satellite signal receiving device.2. A satellite system according to claim 1, wherein said frequencymeasuring device comprises a phase-lock loop receiver.
 3. A satellitesystem according to claim 1, wherein said frequency measuring device andsaid GPS receiver carry out several measurements of the radio wavesignals emitted from the same signal source during the movement of saidorbiting satellite, on and along the same orbit, on which the frequencymeasuring device and the GPS receiver are provided so that themeasurement data of each measurement if stored in said memory.
 4. Asatellite system according to claim 1, wherein said orbit of theorbiting satellite is one of a polar orbit and a sub-recurrent orbit. 5.A satellite system according to claim 1, wherein said computer measuresthe position of the signal source based on reference frequency data ofthe radio wave signal emitted from the signal source; wherein thefrequency data is measured by the frequency measuring device, and theposition data of the orbiting satellite is measured by the GPS receiver.6. A satellite system according to claim 1, wherein when the radio wavesignal of the predetermined frequency is emitted, said signal sourcesends an identification signal to identify the signal source by theradio wave signal.
 7. A satellite system comprising: a signal sourcelocated on or in at least one of a surface of the earth, a watersurface, and the air; and an orbiting satellite for measuring a positionof said signal source, said orbiting satellite including a GPS receiverwhich receives a GPS signal from a GPS stationary satellite, a frequencymeasuring device for receiving a radio wave signal emitted from a groundsignal source on the earth to measure the frequency of the radio wavesignal, a memory for storing frequency data measured and obtained by thefrequency measuring device and position data measured and obtained bythe GPS receiver upon measurement of said frequency, and a satellitetransmitting device for transmitting the data stored in the memorytoward a ground station; wherein said orbiting satellite comprises asatellite signal receiving device for receiving the radio wave signalemitted from the ground station; said ground station comprises aground-station transmitting device for transmitting a specific commandto send the data stored in the memory of the orbiting satellite; andsaid orbiting satellite transmits the data stored in the memory throughthe satellite transmitting device upon receipt of the specific commandthrough the satellite signal receiving device.
 8. A satellite systemaccording to claim 7, wherein said frequency measuring device comprisesa phase-lock loop receiver.
 9. A satellite system according to claim 7,wherein said frequency measuring device and said GPS receiver carry outseveral measurements of said radio wave signals emitted from the samesignal source during the movement of the orbiting satellite, on andalong the same orbit, on which the frequency measuring device and theGPS receiver are provided so that the measurement data of eachmeasurement is stored in the memory.
 10. A satellite system according toclaim 9, wherein the orbit of the orbiting satellite is a polar orbit.11. A satellite system according to claim 9, wherein when the radio wavesignal of the predetermined frequency is emitted, said signal sourcesends an identification signal to identify the signal source by theradio wave signal.